Question

The function f is defined for  by .

                    i.       Find  and .

The first, second and third terms of a geometric progression are respectively ,   and .

                  ii.       Find the value of the constant k.

Solution

     i.
 

We are given the function;

Therefore;

Rule for differentiation of  is:

Therefore;

Second derivative is the derivative of the derivative. If we have derivative of the curve   as  , then  expression for the second derivative of the curve  is;

Rule for differentiation of  is:

ii.
 

We are given that the first, second and third terms of a geometric progression are respectively ,    and .

Let’s find first three terms of the Geometric Progression (G.P).

Hence, first three terms of the Geometric Progression (G.P).

Expression for Common Ratio () in a Geometric Progression (G.P) is;